On the Local Regularity of the Hilbert Transform

TL;DR

This paper investigates the local regularity properties of the Hilbert transform, establishing results on its local smoothness and real analyticity in various contexts.

Contribution

It provides new insights into the local regularity and analyticity of the Hilbert transform, extending previous understanding of its smoothness properties.

Findings

Established local smoothness of the Hilbert transform.

Proved real analyticity under certain conditions.

Extended regularity results to broader function classes.

Abstract

In this paper the local regularity of the Hilbert transform is considered, and local smoothness and real analyticity results are obtained.